The Study Of The Topology Of Nonlinear Growing Complex Networks

Evolution theory is an important research field of complex networks. A major of previous network evolution models usually assume that the networks grow in a linear way. However, empirical data shows that the growth of many real networks is nonlinear, i.e., accelerating. Aiming at this case, a general nonlinear growth model is proposed in this thesis. The growth rate of edges and vertices are power law function of time. It is found that the fraction of the internal edges plays a crucial role to influence the structure of the network. An important difference of our model from other accelerated networks or linear growth networks is that the accelerated growth of nodes will have nontrivial effects on the topology of the network. The degree distribution, clustering coefficient and degree assortative coefficient are all relevant to the growth rate of edges and vertices.The increasing information flow (or traffic flow) as an internal demand always spurs the expansion of networks (e.g. Internet and WWW etc.). The nonlinear growth mechanism is originally introduced into weighted-networks in this thesis. The author make a comprehensive analysis of the statistical characteristics of the degree, strength, weight, clustering and assortative mixing which are all depend on the growth rate of internal weights.The nonlinear growth of networks is more common than the linear growth. In many situations, it is impossible to understand the feature of an evolving network without accounting for this mechanism. The present work is advantageous to the research of network evolution theory, as well as the study of the coupling between information flow and topology of the complex networks in the future.